Advanced Networks Colloquium: Muriel Medard, "Information Theory Variations: Patterns in Security"
Friday, February 12, 2016
1146 A.V. Williams Building
The Advanced Networks Colloquium
Two recent information theoretic variations on the theme of patterns in security
Cecil H. Green Professor
Electrical Engineering and Computer Science Department
Massachusetts Institute of Technology
We overview two different sets of results based upon the effect of patters in security. In the first part, we consider limits of inference, a problem that emerges when we seek to ascertain what limits to privacy we can expect when machine learning algorithms, whose theoretical basis often relies on principal inertia components, are applied to mining publicly available data that may be related, in loosely known ways, to private data. Lower bounds for the average probability of error of estimating a hidden variable X given an observation of a correlated random variable Y, and Fano’s inequality in particular, play a central role in information theory. We present a lower bound for the average estimation error based on the marginal distribution of X and the principal inertias of the joint distribution matrix of X and Y, providing thus limits to privacy. Furthermore, we investigate how to answer a fundamental question in inference and privacy: given an observation Y, can we estimate a function f(X) of the hidden random variable X with an average error below a certain threshold? We provide a general method for answering this question using an approach based on rate-distortion theory. In the second part, we consider recent results on guesswork, the characterization of the process sequences such as passwords. We note that, what may appear as being even slight differences in distributions of these sequences may lead to differences that are exponential in guesswork, leading to possible surprising results, such as the failure of the oft-assumed uniformity of compressed sources, and the fact that friendly jamming of an intended user may be advantageous. We conclude with our recently defined notion of inscrutability rate, used to quantify the asymptotic difficulty of guessing U out of V secret strings, Unexpectedly, the inscrutability rate of any finite-order Markov string-source with hidden statistics remains the same as the unhidden case, i.e., the asymptotic value of hiding the statistics per each symbol is vanishing.
Joint work with Ahmad Beirami, Robert Calderbank, Flavio du Pin Calmon, Mark Christiansen, Ken Duffy, Stefano Tessaro, Mayank Varia.
Muriel Médard is the Cecil H. Green Professor in the Electrical Engineering and Computer Science Department at MIT and leads the Network Coding and Reliably Communications Group at the Research Laboratory for Electronics at MIT. She has co-founded two companies to commercialize network coding, CodeOn and Steinwurf. She has served as editor for many publications of the Institute of Electrical and Electronics Engineers (IEEE), of which she was elected Fellow, and she is currently Editor in Chief of the IEEE Journal on Selected Areas in Communications She was President of the IEEE Information Theory Society in 2012, and served on its board of governors for eleven years. She has served as technical program committee co-chair of many of the major conferences in information theory, communications and networking. She received the 2009 IEEE Communication Society and Information Theory Society Joint Paper Award, the 2009 William R. Bennett Prize in the Field of Communications Networking, the 2002 IEEE Leon K. Kirchmayer Prize Paper Award and several conference paper awards. She was co-winner of the MIT 2004 Harold E. Edgerton Faculty Achievement Award. In 2007 she was named a Gilbreth Lecturer by the U.S. National Academy of Engineering.